Artech digital modulation techniques MAZ

For each modulation scheme, the following topics are covered: historical background, operation principles, symbol and bit error performance power efficiency, spectral characteristic band

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Fuqin Xiong

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Digital modulation techniques / Fuqin Xiong.

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ISBN 0-89006-970-0 (alk paper)

1 Digital modulation I Title II Series.

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10 9 8 7 6 5 4 3 2 1

3.2 Coherent Demodulation and Error Performance 95 3.3 Noncoherent Demodulation and Error Performance 98

3.4.1 MFSK Signal and Power Spectral Density 102 3.4.2 Modulator, Demodulator,

5.2.2 Bandwidth of MSK and Comparison with PSK 204

5.11 Rabzel and Pathupathy's Symbol-Shaping Pulses 247

viii 6.1.3 Phase Tree and Trellis, State Trellis 269

6.2.1 Steps for Calculating PSDs

6.2.2 Effects of Pulse Shape, Modulation Index,

6.3.1 Error Probability and Euclidean Distance 281

6.5.8 Differential and Discriminator Demodulator 330

6.6.2 Squaring Loop and Fourth-Power Loop

7.3 Distance Properties and Error Probability 366

7.5.1 A Simple ML Demodulator for Multi-h

Synchronization of Multi-h CPFSK 388 7.5.3 Joint Carrier Phase Tracking and Data

8.1.2 Optimum Detection and Error Probability 414 8.1.3 Modulator and Demodulator for Bandpass MAM 418

Chapter 10 Performance of Modulations in Fading Channels 517

10.2 Digital Modulation in Slow, Flat Fading Channels 527

10.3 Digital Modulation in Frequency Selective Channels 533

Appendix A Power Spectral Densities of Signals 567

A.2 Bandpass Stationary Random Process and PSD 569 A.3 Power Spectral Densities of Digital Signals 572 A.3.1 Case 1: Data Symbols Are Uncorrelated 574

A.4 Power Spectral Densities of Digital Bandpass Signals 577

B.2 Detection of Continuous Signals With Known Phases 596

Digital modulation techniques are essential to many digital communication systems, whether it is a telephone system, a mobile cellular communication system, or a satellite communication system In the past twenty years or so, research and development in digital modulation techniques have been very active and have yielded many promising results However, these results are scattered all over the literature As a result, engineers and students in this field usually have difficulty locating particular techniques for applications or for research topics This book provides readers with complete, up-to-date information of all modulation techniques in digital communication systems There exist numerous textbooks of digital communications, each of them containing one or more chapters of digital modulation techniques covering either certain types of modulation, or only principles of the techniques There are also a few books

specializing in certain modulations This book presents principles and applications information of all currently used digital modulation techniques, as well as new techniques now being developed For each modulation scheme, the following topics are covered: historical background, operation principles, symbol and bit error performance (power efficiency), spectral characteristic (bandwidth efficiency), block diagrams of modulator, demodulator, carrier recovery (if any), clock recovery, comparison with other schemes, and applications After we fully understand the modulations and their performances in the AWGN channel, we will discuss their performances in rnultipath-fading channels

Organization of the book

This book is organized into 10 chapters Chapter 1 is an introduction for those requiring basic knowledge about digital communication systems, and modulation methods

Chapter 2 is about baseband signal modulation that does not involve a carrier

X l l l

s i v Digital Modulation Techniques

It is usually called baseband signal formatting or line coding Traditionally the

term modzrlation refers to "impression of message on a carrier," however, if we

widen the definition to "impression of message on a transmission medium," this format~ing is also a kind of modulation Baseband modulation is important not only because it is used in short distance data communications, magnetic recording optical recording, etc., but also because it is the front end of bandpass modulations

Chapters 3-4 cover classical frequency shift keying (FSK) and phase shift keying (PSK) techniques, including coherent and noncoherent These techniques are currently used in many digital communication systems, such as cellular digital telephone systems, and satellite communication systems

Chapters 5-7 are advanced phase modulation techniques which include minimum shift keying (MSK), continuous phase modulation (CPM), and multi-h phase modulation (MHPM) These techniques are the research results of recent years, and some of them are being used in the most advanced systems, for example, MSK has been used in NASA's Advanced Communications Technology Satellite (ACTS) launched in 1993, and the others are being perfected for future applications

Chapter 8 is about quadrature amplitude modulation (QAM) QAM schemes are widely used in telephone modems For instance, CCITT (Consultative Committee for International Telephone and Telegraph) recommended V.29 and

V.33 modems use 16- and 128-QAM, reaching speeds of 9600 bps and 14400 bps respectively, over four-wire leased telephone lines

Chapter 9 covers nonconstant-envelope bandwidth-efficient modulation schemes We will study eight schemes, namely, QBL, QORC, SQORC, QOSRC, IJF-OQPSK, TSI-OQPSK, SQAM and Q~PSK These schemes improve the power spectral density with little loss in error probability They are primarily designed for satellite communications

Chapter 10 first briefly introduces characteristics of channels with fading and multipath propagation Then all modulations discussed in Chapters 2-8 are examined under the fading-muhi path environment

Appendixes A and B are basic knowledge of signal spectra and classical signal detection and estimation theory

This book can be used as a reference book for engineers and researchers It also can be used as a textbook for graduate students The material in the book can

be covered in a half-year course For short course use, the instructor may select relevant chapters to cover

First I would like to thank the reviewers and editors at Artech House, Ray Sperber, Mark Walsh, Barbara Lovenvirth, and Judi Stone, whose many critiques and suggestions based on careful reviews contributed to the improvement of the manuscript

I would like to thank Cleveland State University and Fenn College of Engineering for granting me the sabbatical leave in 1997 during which 1 wrote a

substantial part of the book I am grateful for the support and encouragement from

many colleagues at the Department of Electrical and Computer Engineering

I am grateful to NASA Glenn Research Center for providing me with several research grants Particularly, the grant for investigating various modulation schemes that resulted in a report which was well received by NASA engineers and researchers Encouraged by their enthusiastic response to the report I published the tutorial paper "Modem Techniques in Satellite Communications" in the l E E E

Comnwzication Magazine, August 1 994 Further, encouraged by the positive response to the tutorial paper, I developed the idea of writing a book detailing all major modulation schemes

I would like to thank Professor Djamal Zeghlache of the Institut National des Telecommunications of France for his support and encouragement to the book

1 would like to thank the Department of Electronics City University of Hong Kong (CUHK), and the Department of Electronics, Tsinghua University, Beijing, China for supporting my sabbatical leave Particularly, I would like to thank Professor Li Ping of CUHK for his suggestions to the book and Professor Cao Zhigang of Tsinghua for his support of the book writing

1 am very grateful to the excellent education that I received from Tsinghua University and the University of Manitoba, Canada Particularly, I would like to thank my doctoral program advisor, Professor Edward Shwedyk of the Department

of Electrical and Computer Engineering, University of Manitoba, and Professor John B Anderson of Electrical, Computer and Systems Engineering Department, Rensselaer Polytechnic Institute, who served in m y doctoral dissertation committee, for their guidance and encouragement

I also appreciate the support and suggestions from my graduate students during the past a few years

Finally, the support and help for the book from my family are also deeply appreciated

Fuqin Xiong

Chapter 1

Introduction

In this chapter we briefly discuss the role of modulation in a typical digital com- munication system, basic modulation methods, and criteria for choosing modulation schemes Also included is a brief description of various communication channels, which will serve as a background for the later discussion of the modulation schemes

Figure 1.1 is the block diagram of a typical digital communication system The mes- sage to be sent may be fiom an analog source (e.g., voice) or fiom a digital source (e.g., computer data) The analog-to-digital (AID) converter samples and quantizes the analog signal and represents the samples in digital form (bit 1 or 0) The source encoder accepts the digital signal and encodes it into a shorter digital signal This is called source encoding, which reduces the redundancy hence the transmission speed This in turn reduces the bandwidth requirement of the system The channel encoder accepts the output digital signal of the source encoder and encodes it into a longer digital signal Redundancy is deliberately added into the coded digital signal so that some of the errors caused by the noise or interference during transmission through the channel can be corrected at the receiver Most often the transmission is in a high- frequency passband, the modulator thus impresses the encoded digital symbols onto

a carrier Sometimes the transmission is in baseband, the modulator is a baseband modulator, also called formator, which formats the encoded digital symbols into a waveform suitable for transmission Usually there is a power amplifier following the modulator For high-frequency transmission, modulation and demodulation are usually performed in the intermediate frequency (IF) If this is the case, a frequency up-convertor is inserted between the modulator and the power amplifier If the IF is too low compared with the carrier frequency, several stages of carrier frequency con- versions are needed For wireless systems an antenna is the final stage of the trans-

of random electrical disturbance from outside or from within the system The chan- nel also usually has a limited frequency bandwidth so that it can be viewed as a filter

In the receiver, virtually the reverse signal processing happens First the received weak signal is amplified (and down-converted if needed) and demodulated Then the added redundancy is taken away by the channel decoder and the source decoder recovers the signal to its original form before being sent to the user A digital-to-

analog (DIA) converter is needed for analog signals

The block diagram in Figure I 1 is just a typical system configuration A real system configuration could be more complicated For a multiuser system, a mul- tiplexing stage is inserted before modulator For a multistation system, a multiple access control stage is inserted before the transmitter Other features like frequency spread and encryption can also be added into the system A real system could be simpler too Source coding and channel coding may not be needed in a simple sys- tem In fact, only the modulator, channel, demodulator, and amplifiers are essential

in all communication systems (with antennas for wireless systems)

For the purpose of describing modulation and demodulation techniques and an-

I

Source decoder -

Chapter I Introdttction

n(t)

additive noise and

-

interference Channel

Figure 1.2 Digital communication system model for modulation and demodulation

alyzing their performance, the simplified system model shown in Figure 1.2 will be often used This model excludes irrelevant blocks with regard to modulation so that relevant blocks stand out However, recently developed modem techniques combine modulation and channel coding together In these cases the channel encoder is part

of the modulator and the channel decoder is part of the demodulator From Figure 1.2, the received signal at the input of the demodulator can be expressed as

where * denotes convolution In Figure 1.2 the channel is described by three ele- ments The first is the channel filter Because of the fact that the signal s ( t ) from the modulator must pass the transmitter, the channel (transmission medium) and the re- ceiver before it can reach the demodulator, the channel filter therefore is a composite filter whose transfer function is

where H T ( f ), Hc( f ), and H R ( f ) are the transfer function of the transmitter, the channel, and the receiver, respectively Equivalently, the impulse response of the channel filter is

where hT(t), hc(t), and h R ( t ) are the impulse responses of the transmitter, the chan- nel, and the receiver, respectively The second element is the factor A ( t ) which is generally complex This factor represents fading in some types of channels, such as mobile radio channel The third element is the additive noise and interference term

n ( t ) We will discuss fading and noise in more detail in the next section The channel

model in Figure 1.2 is a general model It may be simplified in some circumstances,

as we will see in the next section

In this section we discuss several important channel models in communications

1.2.1 Additive White Gaussian Noise Channel

Additive white Gaussian noise (AWGN) channel is a universal channel model for analyzing modulation schemes In this model, the channel does nothing but add a white Gaussian noise to the signal passing through it This implies that the channel's amplitude frequency response is flat (thus with unlimited or infinite bandwidth) and phase frequency response is linear for all frequencies so that modulated signals pass through it without any amplitude loss and phase distortion of frequency components Fading does not exist The only distortion is introduced by the AWGN The received signal in ( I I ) is simplified to

where n ( t ) is the additive white Gaussian noise

The whiteness of n ( t ) implies that it is a stationary random process with a flat power spectral density (PSD) for all frequencies It is a convention to assume its PSD as

This implies that a white process has infinite power This of course is a mathemat- ical idealization According to the Wiener-Khinchine theorem, the autocorrelation function of the AWGN is

where & ( T ) is the Dirac delta function This shows the noise samples are uncorrelated

where

and

The variance of n is

Then the probability density function (PDF) of n can be written as

This result will be frequently used in this book

Strictly speaking, the AWGN channel does not exist since no channel can have an infinite bandwidth However, when the signal bandwidth is smaller than the channel bandwidth, many practical channels are approximately an AWGN channel For ex- ample, the line-of-sight (LOS) radio channels, including fixed terrestrial microwave links and fixed satellite links, are approximately AWGN channels when the weather

is good Wideband coaxial cables are also approximately AWGN channels since there

is no other interference except the Gaussian noise

In this book, all modulation schemes are studied for the AWGN channel The reason of doing this is two-fold First, some channels are approximately an AWGN channel, the results can be used directly Second, additive Gaussian noise is ever present regardless of whether other channel impairments such as limited bandwidth, fading, multipath, and other interferences exist or not Thus the AWGN channel is the best channel that one can get The performance of a modulation scheme evaluated in this channel is an upper bound on the performance When other channel impairments exist, the system performance will degrade The extent of degradation may vary for different modulation schemes The performance in AWGN can serve as a standard

in evaluating the degradation and also in evaluating effectiveness of impairment- combatting techniques

1.2.2 Bandlimited Channel

When the channel bandwidth is smaller than the signal bandwidth, the channel is bandlimited Severe bandwidth limitation causes intersymbol interference (ISI) (i.e., digital pulses will extend beyond their transmission duration (symbol period T s ) ) and

interfere with the next symbol or even more symbols The IS1 causes an increase

in the bit error probability (Pb) or bit error rate (BER), as it is commonly called When increasing the channel bandwidth is impossible or not cost-efficient, channel equalization techniques are used for combatting ISI Throughout the years, numerous equalization techniques have been invented and used New equalization techniques are appearing continuously We will not cover them in this book For introductory treatment of equalization techniques, the reader is referred to [ I Chapter 6 ) or any other communication systems books

Chapter 1 Intmduction

Fading is a phenomena occurring when the amplitude and phase of a radio signal change rapidly over a short period of time or travel distance Fading is caused by in- terference between two or more versions of the transmitted signal which arrive at the receiver at slightly different times These waves, called multipath waves, combine

at the receiver antenna to give a resultant signal which can vary widely in amplitude and phase If the delays of the multipath signals are longer than a symbol period, these multipath signals must be considered as different signals In this case, we have individual multipath signals

In mobile communication channels, such as terrestrial mobile channel and satel- lite mobile channel, fading and multipath interference are caused by reflections from surrounding buildings and terrains In addition, the relative motion between the transmitter and receiver results in random frequency modulation in the signal due

to different Doppler shifts on each of the multipath components The motion of surrounding objects, such as vehicles, also induces a time-varying Doppler shift on multipath component However, if the surrounding objects move at a speed less than the mobile unit, their effect can be ignored [2]

Fading and multipath interference also exist in fixed LOS microwave links [3]

On clear, calm summer evenings, normal atmospheric turbulence is minimal The troposphere stratifies with inhomogeneous temperature and moisture distributions Layering of the lower atmosphere creates sharp refractive index gradients which in turn create multiple signal paths with different relative amplitudes and delays Fading causes amplitude fluctuations and phase variations in received signals Multipath causes intersymbol interference Doppler shift causes carrier frequency drift and signal bandwidth spread All these lead to performances degradation of modulations Analysis of modulation performances in fading channels is given in Chapter 10 where characteristics of fading channels will be discussed in more detail

1.3 BASIC MODULATION METHODS

Digital modulation is a process that impresses a digital symbol onto a signal suitable for transmission For short distance transmissions, baseband modulation is usually used Baseband modulation is often called line coding A sequence of digital sym- bols are used to create a square pulse waveform with certain features which represent each type of symbol without ambiguity so that they can be recovered upon reception These features are variations of pulse amplitude, pulse width, and pulse position Figure 1.3 shows several baseband modulation waveforms The first one is the non- return to zero-level (NRZ-L) modulation which represents a symbol 1 by a positive

(b) Unipolar RZ

(c) Bi-a-L (Manchester)

Figure 1.3 Baseband digital modulation examples

square pulse with length T and a symbol 0 by a negative square pulse with length T The second one is the unipolar return to zero modulation with a positive pulse of T/2 for symbol I and nothing for 0 The third is the biphase level or Manchester, after its inventor, modulation which uses a waveform consisting of a positive first-half T pulse and a negative second-half T pulse for 1 and a reversed waveform for 0 These and other baseband schemes will be discussed in detail in Chapter 2

For long distance and wireless transmissions, bandpass modulation is usually used Bandpass modulation is also called carrier modulation A sequence of dig- ital symbols are used to alter the parameters of a high-frequency sinusoidal signal called carrier It is well known that a sinusoidal signal has three parameters: am- plitude, frequency, and phase Thus amplitude modulation, frequency modulation, and phase modulation are the three basic modulation methods in passband modula- tion Figure 1.4 shows three basic binary carrier modulations They are amplitude shift keying (ASK), frequency shift keying (FSK), and phase shift keying (PSK) In ASK, the modulator puts out a burst of carrier for every symbol 1, and no signal for every symbol 0 This scheme is also called on-off keying (OOK) In a general ASK scheme, the amplitude for symbol 0 is not necessarily 0 In FSK, for symbol

I a higher frequency burst is transmitted and for symbol 0 a lower frequency burst

Figure 1.4 Three basic bandpass modulation schemes

is transmitted, or vice versa In PSK, a symbol I is transmitted as a burst of carrier with 0 initial phase while a symbol 0 is transmitted as a burst of carrier with 180'

initial phase

Based on these three basic schemes, a variety of modulation schemes can be de- rived from their combinations For example, by combining two binary PSK (BPSK) signals with orthogonal carriers a new scheme called quadrature phase shift keying (QPSK) can be generated By modulating both amplitude and phase of the carrier,

we can obtain a scheme called quadrature amplitude modulation (QAM), etc

The essence of digital modem design is to efficiently transmit digital bits and recover them from corruptions from the noise and other channel impairments There are three primary criteria of choosing modulation schemes: power efficiency, bandwidth

efficiency, and system complexity

1.4.1 Power Efficiency

The bit error rate, or bit error probability of a modulation scheme is inversely related

to E b / S , , the bit energy to noise spectral density ratio For example, Pb of ASK in the AWGN channel is given by

(I 10)

where Eb is the average bit energy, No is the noise power spectral density (PSD), and

Q ( s ) is the Gaussian integral, sometimes referred to as the Q-function It is defined

as

which is a monotonically decreasing function of x Therefore the power efficiency

of a modulation scheme is defined straightforwardly as the required Eb/Ar0 for a certain bit error probability (Pb) over an AWGN channel Pb = lo-' is usually used

as the reference bit error probability

1 A.2 Bandwidth Efficiency

The determination of bandwidth efficiency is a bit more complex The bandwidth efficiency is defined as the number of bits per second that can be transmitted in one Hertz of system bandwidth Obviously it depends on the requirement of system bandwidth for a certain modulated signal For example, the one-sided power spectral density of an ASK signal modulated by an equiprobable independent random binary sequence is given by

and is shown in Figure 1.5, where T is the bit duration, A is the carrier amplitude, and f, is the carrier frequency From the figure we can see that the signal spectrum stretches from -m to OG Thus to perfectly transmit the signal an infinite system bandwidth is required, which is impractical The practical system bandwidth require- ment is finite, which varies depending on different criteria For example, in Figure 1.5, most of the signal energy concentrates in the band between two nulls, thus a null-to-null bandwidth requirement seems adequate Three bandwidth efficiencies

Chapter I Introduction

Figure I .5 Power spectral density of ASK

used in the literature are as follows:

Nyquist Bandwidth Efficiency-Assuming the system uses Nyquist (ideal rec- tangular) filtering at baseband, which has the minimum bandwidth required for in- tersyrnbol interference-free transmission of digital signals, then the bandwidth at baseband is 0.5RS, Rs is the symbol rate, and the bandwidth at carrier frequency

is W = R, Since R, = Rb/ log, M, Rb = bit rate, for M-ary modulation, the bandwidth efficiency is

Null-to-Null Bandwidth Efficiency-For modulation schemes that have power density spectral nulls such as the one of ASK in Figure 1.5, defining the bandwidth

as the width of the main spectral lobe is a convenient way of bandwidth definition Percentage Bandwidth Efficiency-If the spectrum of the modulated signal does not have nulls, as in general continuous phase modulation (CPM), null-to-null bandwidth no longer exists In this case, energy percentage bandwidth may be used Usually 99% is used, even though other percentages (e.g., 90%, 95%) are also used

1.4.3 System Complexity

System complexity refers to the amount of circuits involved and the technical dif- ficulty of the system Associated with the system complexity is the cost of manu-

facturing, which is of course a major concern in choosing a modulation technique Usually the demodulator is more complex than the modulator Coherent demodula- tor is much more complex than noncoherent demodulator since carrier recovery is required For some demodulation methods, sophisticated algorithms like the Viterbi algorithm is required All these are basis for complexity comparison

Since power efficiency, bandwidth efficiency, and system complexity are the main criteria of choosing a modulation technique, we will always pay attention to them in the analysis of modulation techniques in the rest of the book

1.5 OVERVIEW OF DIGITAL MODULATION SCHEMES

To provide the reader with an overview, we list the abbreviations and descriptive names of various digital modulations that we will cover in Table 1.1 and arrange them in a relationship tree diagram in Figure 1.6 Some of the schemes can be derived from more than one "parent" scheme The schemes where differential encoding can

be used are labeled by letter D and those that can be noncoherently demodulated are labeled with a letter N All schemes can be coherently demodulated

The modulation schemes listed in the table and the tree are classified into two large categories: constant envelope and nonconstant envelope Under constant en- velope class, there are three subclasses: FSK, PSK, and CPM Under nonconstant envelope class, there are three subclasses: ASK, QAM, and other nonconstant enve- lope modulations

Among the listed schemes, ASK, PSK, and FSK are basic modulations, and MSK, GMSK, CPM, MHPM, and QAM, etc are advanced schemes The advanced schemes are variations and combinations of the basic schemes

The constant envelope class is generally suitable for communication systems whose power amplifiers must operate in the nonlinear region of the input-output characteristic in order to achieve maximum amplifier efficiency An example is the TWTA (traveling wave tube amplifier) in satellite communications However, the generic FSK schemes in this class are inappropriate for satellite application since they have very low bandwidth efficiency in comparison with PSK schemes Binary FSK

is used in the low-rate control channels of first generation cellular systems, AMPS (advance mobile phone service of US.) and ETACS (European total access commu- nication system) The data rates are 10 Kbps for AMPS and 8 Kbps for ETACS The PSK schemes, including BPSK, QPSK, OQPSK, and MSK have been used in satellite communication systems

The TI?-QPSK is worth special attention due to its ability to avoid 180" abrupt phase shift and to enable differential demodulation It has been used in digital mobile cellular systems, such as the United States digital cellular (USDC) system

Chapter I Introduction

Abbreviation I Alternate Abbr I Descriptive name

Frequency Shift Keying (FSK)

Binary Frequency Shift Keying M-ary Frequency Shift Keying

4PSK SQPSK

Phase Shift Keying (PSK) PSK I Binary Phase Shift Keying

~uadrature ~ h & e Shift Keying Offset QPSK, Staggered QPSK

SHPM

Continuous Phase Modulations (CPM)

I Single-h (modulation index) Phase Modulation MHPM

LREC

Multi-h Phase Modulation Rectangular Pulse of Length L CPFSK

Arn~litude and Am~litudePhase modulations

Nonconstant Envelope Modulations

MAM M-ary ASK, M-ary Amplitude Modulation

Quadrature Amplitude Modulation

QOSRC

Q ~ P S K

IJF-OQPSK

Table 1.1 Digital modulation schemes (Abbr.=Abbreviation)

Quadrature Overlapped Squared Raised Cosine Modulation Quadrature Quadrature Phase Shift Keying

Intersymbol-InterferencdJitter-Free OQPSK TSI-OQPSK

SQAM

XPSK

7

Two-Symbol-Interval OQPSK Superposed-QAM

Crosscorrelated QPSK

I Digital Modulations (

Constant Envelope

Solid lines indicate "can be derived fkorn"

- - - Dashed lines indicate "alternatively can be derived from"

Can be differentially encoded and decoded

Can be noncoherently detected

Chapter l Introduction 15

The PSK schemes have constant envelope but discontinuous phase transitions from symbol to symbol The CPM schemes have not only constant envelope, but also continuous phase transitions Thus they have less side lobe energy in their spectra

in comparison with the PSK schemes The CPM class includes LREC, LRC, LSRC, GMSK, and TFM Their differences lie in their different frequencypulses which are reflected in their names For example, LREC means the Frequency pulse is a rectan- gular pulse with a length of L symbol periods MSK and GMSK are two important schemes in CPM class MSK is a special case of CPFSK, but it also can be derived from OQPSK with extra sinusoidal pulse-shaping MSK has excellent power and bandwidth efficiency Its modulator and demodulator are also not too complex MSK has been used in NASA's Advanced Communication Technology Satellite (ACTS) GMSK has a Gaussian frequency pulse Thus it can achieve even better bandwidth efficiency than MSK GMSK is used in the US cellular digital packet data (CDPD) system and European GSM (global system for mobile communication) system MHPM is worth special attention since it has better error performance than single-h CPM by cyclically varying the modulation index h

The generic nonconstant envelope schemes, such as ASK and QAM, are gen- erally not suitable for systems with nonlinear power amplifiers However QAM, with a large signal constellation, can achieve extremely high bandwidth efficiency

Q A M has been widely used in modems used in telephone networks, such as computer modems QAM can even be considered for satellite systems In this case, however, back-off in TWWs input and output power must be provided to ensure the linearity

of the power amplifier

The third class under nonconstant envelope modulation includes quite a few schemes These are primarily designed for satellite applications since they have very good bandwidth efficiency and the amplitude variation is minimal All of them ex- cept Q ~ P S K are based on 2Ts amplitude pulse shaping and their modulator structures are similar to that of OQPSK The scheme Q'PSK is based on four orthogonal car- riers

References

[ 1 1 Proakis, J.? Digital Communication, New York: McGraw-Hill 1983

12) Rappaport T tKreless Communications: Principles and Practice, Upper Saddle River New

Jersey: Prentice Hall 1996,

131 Siller, C "Multipath propagation," IEEE Communications Jlagazine, vol 22 no.2 Feb I 984

pp 6-15

[4] Xiong F "Modem techniques in satellite communications." IEEE Communications \!againe

vol 3 2 , no.8 August 1994, pp 84-98

S klar B Digital Communications, Fundamentals and Applications, Englewood Cliffs New

Jersey: Prentice Hall, 1988

Chapter 2

Baseband Modulation (Line Codes)

Baseband modulation is defined as a direct transmission without Frequency trans- form It is the technology of representing digital sequences by pulse waveforms suitable for baseband transmission A variety of waveforms have been proposed

in an effort to find ones with some desirable properties, such as good bandwidth and power efficiency, and adequate timing information These baseband modula- tion waveforms are variably called line codes, baseband formots (or waveforms),

PCM waveforms (orformats, or codes ) PCM (pulse code modulation) refers to the process that a binary sequence representing a digitized analog signal is coded into

a pulse waveform For a data signal PCM is not needed Therefore the terms line code and baseband format (or waveform) are more pertinent and the former one is more often used Line codes were mainly developed in the 1960s by engineers at

AT&T, IBM or RCA for digital transmission over telephone cables or digital record- ing on magnetic media [MI Recent developments in line codes mainly concentrate

on fiber optic transmission systems [HI I

In this chapter we first introduce differential coding technique which is used in the later part of the chapter in constructing line codes Then we describe various basic line codes in Section 2.2 Their power spectral densities are discussed in Section 2.3 The demodulation of these waveforms is in effect a detection problem of signals

in noise In Section 2.4 we first describe optimum detection of binary signals in

additive white Gaussian noise (AWGN) and then apply the resultant general formulas

to obtain expressions for bit error probabilities or bit error rates (BER) of various line codes The general results can be used for any binary signal, including bandpass signals which will be described in later chapters It also should be pointed out that practical detectors for line codes are often not optimum in order to simplify circuitry However, the performance of an optimum detector can always serve as a reference for comparison Substitution codes and block line codes are more complicated codes with improved performance over basic line codes They are discussed in Sections

2.5 and 2.6 Section 2.7 summarizes this chapter Intersymbol interference (ISI)

phenomena and equalization techniques, including duobinary signaling technique, are important topics in baseband signaling techniques, whether bandpass modulation

is followed or not An in-depth coverage of these topics requires a large number of pages and is therefore not included in this book which i s intended for modulation schemes For introductory knowledge of IS1 and equalization the reader can refer to any text book on digital communications

2.1 DIFFERENTIAL CODING

Since some of the baseband binary waveforms use a technique called diffeerential encoding we need become familiar with this simple yet important baseband tech- nique This technique is not only used in baseband modulation but also in bandpass modulation where it is used to encode the baseband data before modulating it onto a carrier The benefit of using differential coding will become clear when we discuss the schemes that use it We now study this technique and it will be used throughout the rest of the book

Let { a k } be the original binary data sequence, then a differentially encoded bi- nary data sequence { d k } is produced according to the rule

where t1> indicates modulo-2 addition Modulo-2 addition is also called exclusive-

OR (XOR) The modulo-2 addition rules are 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and

1 + 1 = 0 From (2.1) and the modulo-2 rules we can see that the current output bit of the encoder is determined by the current input bit and the previous output bit

If they are different the output bit is 1, otherwise the output bit is 0 This gives the name differential encoding

To perform differential encoding an initial bit is needed and it is called a refer-

ence bit For example, if { a k } and I d k } both start with k = 1, then we need a do as the reference bit Since do could be chosen as 0 or 1, then {ak} can be encoded into two different data sequences They are complementary to each other

The decoding rule is

where the hat indicates the received data at the receiver The received { & } could be the same as or different from {dk} For example channel noise might have altered some of the bits in { d k } when it is received Even if noise is light so that no bits have been altered by noise, the polarity reversals in various stages of the transmitter and receiver might have reversed the polarity of the entire sequence One of the

Chapter 2 Baseband Modulation (Line Codes) 19

Table 2.1 Examples of differential coding

important uses of differential coding is to eliminate the effect of polarity reversal This is clear from (2.2) since the decoder output depends on the difference of the two consecutive received bits, not their polarities When the polarity of the entire sequence is altered, the difference between two consecutive bits remains the same Table 2.1 is an example which illustrates the encoding and decoding processes with

or without polarity reversal The results are the same Note that no errors caused by noise are assumed in the example The first bit of {dk} is the reference bit which is

0 in the example

Figure 2.1 shows the block diagrams of the differential encoder and decoder defined by (2.1) and (2.2)

The probability distribution of the differentially encoded sequence is of interest

It is usehl when the autocorrelation function of the coded sequence is calculated later

in the chapter Assume the data sequence {ak} is stationary, its bits are independent and with a distribution of ( p o , p l ) , where po = Pr(0) and pl = Pr(l), po + pl = 1

(k) (k)

Assume the distribution of the kth bit of the coded sequence Idk} is (q, q, ) where gik) = Pr(0) and qik) = Pr(l), g r ) + q ! k ) = 1 According to (2.1) we have

Since an initial bit is specified when encoding, q?) and g\o) are known They are

either 0 or 1, depending on what is chosen For instance, if the reference is 0, then

= 1, q!') = 0 It is easy to verify that if po = pl = 112, then q r ) = q\k) =

112, for all k That is, differential encoding does not change data distribution for equally likely data However, when the distribution of the original data is not equal, differential encoding does change the data distribution Further we can show that

Figure 2.1 Differential encoder (a), and decoder (b)

qc) = qik) = 112 asymptotically regardless of values of po and pl

We start with any one of the above two equations, say (2.3), from which we have

Taking a r-transform of both sides of the above equation, we obtain

( k )

where Q o ( z ) is the t-transform of sequence {qo } Rearranging terms we have

Using the final-value theorem we obtain the limit of qr) as

Chapter 2 Baseband Modulation (Line Codes)

and substituting (2.3) and (2.4) into the r k expression we have

Next we define the ratio difference as

If A r k + 0, then rk + r k - 1 solving (2.5) will give rk = 1 (i.e., qik) = qAk) for

k + m)

Calculations show that for po = 0.3 and 0.1, qik) virtually equals q r ) ( a r k <

0.001) at k = 10 and 38, respectively For a very skewed distribution ( e g , po = 0.01), to reach A r k < 0.001,411 iterations are needed Ail these k values are small when compared with numbers of data in practical systems Thus we can see that the distribution of the differentially encoded data becomes virtually equal very quickly, regardless of the distribution of the original data,

Differential encoding can also be done by taking the binary complement of the modulo-2 adder as the output, that is

where ir denotes a binary complement of x Again this second rule can generate two complementary sequences with the two different choices of the reference bit The corresponding decoding rule is

which is also capable of correcting polarity reversals The block diagrams of the encoder and the decoder defined by this set of rules are similar to that in Figure 2.1 except that an inverter is needed at the output of both encoder and decoder

The above argument about distribution also applies to data encoded this way since this coded sequence is just a complement of the previous one

Another type of differential encoding is

which produces a three-level sequence (- 1,0! + 1) An arbitrary initial reference bit

a, must be specified It is obvious that the distribution of dk is

1, ql = p l p o , for ak-1 = 1 and ak = 0

d k = { -1, 9-1 = popl, for ak-1 = 0 and a k = 1

0, qo=pg+p:, f o r a k _ l = a k = ~ o r l

Decoding can be done as follows First {& } is converted to unipolar {Gk} by full-wave rectification, then {Ck} is recovered from {Ck} by XOR operation:

where the initial Eo = a, is known This coding scheme is also immune fiom polarity inversion-ambiguity problem since after full-wave rectification, the waveform would

be the same

2.2 DESCRIPTION OF LINE CODES

Many binary line codes have been proposed in the literature and some of them have been used in practical systems 11-1 11 Basic codes can be classified into four classes:

nonmturn-to-zero (NRZ), return-to-zero (RZ), pseudoternary (P T), and biphase N RZ and RZ classes can be further divided into unipolar and polar subclasses Advanced codes include substitution codes and block codes There are some other codes which

do not belong to any of the classes Some codes may belong to more than one class Figure 2.2 is a quite complete collection of waveforms of various basic line codes Each of them will be studied in detail shortly Figure 2.2 does not include substitu- tion codes and block codes They will be studied separately in the latter part of this chapter

The reason for the large selection of line codes is because of their differences

in performance which will lead to different applications The features to look for in choosing a line code are as follows For a particular application, some of the features may be important while others may be not

fiom the received data sequence This requires that the line code format provides adequate transition density in the coded sequence Formats with higher transition density are preferable since the timing recovery will have fewer problems with these kinds of signals A long string of binary 1 s and 0s in the data should not cause a problem in timing recovery

( 2 ) A spectrum that is suitable for the channel For example, line codes with

no dc component and small near-dc components in their power spectral density (PSD) are desirable for magnetic recording systems, ac coupled channels, or systems using transformer coupling which have very poor low fiequency responses In addition the PSD of the line code should have sufficiently small bandwidth compared with the channel bandwidth so IS1 will not be a problem

( 3 ) Narrow bandwidrh The bandwidth of the line code should be as narrow

Chapter 2 Baseband Modulation (Line Codes)

Figure 2.2 Line codes After [ 1 21

as possible The transmission bandwidth may be reduced by filtering and multilevel transmission schemes The penalty is an increase in Pb due to

an increase in IS1 and a decrease in signal-to-noise ratio Some line codes may suffer less degradation than others

Low errorprobability The line code can be recovered with low bit error

probability ( P b ) from noise andlor IS1 corrupted received signal The ones with lower Pb for the same average bit energy are usually preferable, but consideration should be given to other characteristics, such as bandwidth and self-timing capability

Error defection capabiliv Some schemes have the capability of detecting

errors in the received sequence without introducing extra bits like in channel coding schemes This error detection capability can be used as

a means of performance monitoring However error correction is not possible, which can only be achieved through channel coding techniques

or automatic retransmission schemes

Bit sequence independence (transparency) The line code must be able to

encode any data sequence from any source and the decoder must be able to decode it back to original data In other words, attributes of the code are independent of the source statistics

Dflerential coding This feature is useful since differentially coded

sequences are immune from polarity inversion as we studied in the previous section However, if differential coding is not inherent in the line code itself, a separate differential coding scheme can be incorporated in the system

In the following we describe the various line codes basically in groups But some of the line codes are singled out due to their importance or unique features When we study these codes the above criteria should be kept in mind, and we will refer to them from time to time

We put emphases on coding rules and characteristics W generally omit coder

and decoder implementations Simple codes can be implemented by simple combi- national and sequential digital circuits, while complex codes can be implemented by digital signal processing techniques A comprehensive coverage on coder and de- coder implementation is not necessary and also is beyond the page limit of this book Interested readers may refer to listed references for circuits However many reported circuits are obsolete already, new circuits should be designed based on new products

of IC chips